We concisely write \( \mathbf {p}^1_{i}(\mathcal {Z}) = \lbrace  \mathbf {p}^1_{i,j}(\mathcal {Z},C) \rbrace _{j = 1}^K \)  and \( \mathbf {p}^2_{i} = \lbrace  \mathbf {p}^2_{i,j}(\mathcal {Z},C) \rbrace _{j = 1}^K \) .
Here, \(\tau \)  is a temperature parameter and we set the value to \(0.1\)  similar to Caron et al., [1]}. Note that, we use \(\mathbf {p}_{i}\)  to denote the predicted cluster assignment probabilities for image \(i\)  (when not referring to a particular view), and a shorthand \(\mathbf {p}\)  is used when \(i\)  is clear from context.
